The latest example came Monday: In Netflix’s May rankings of U.S. Internet service providers, Verizon’s fiber optic “FiOS” service dropped below Windstream Communications’ and Frontier Communications’ slower-speed DSL services. The index measures average Netflix streaming speeds through various broadband providers. Verizon’s DSL service came in dead last.

The FiOS network allows for fast connections between Verizon and customers’ homes. The congestion that is affecting Netflix users is happening at the edge of Verizon’s network, at points where Internet middlemen carrying Netflix traffic are connecting to the telecom company’s network.

The slowdown on Verizon seems puzzling because about a month ago, Netflix struck a deal with the phone giant to link up its servers directly to Verizon’s network – a move that theoretically would lead to improved service for Netflix users. But those links aren’t live yet for Verizon, so Netflix’s video quality worsened last month for millions of FiOS and DSL customers.

A Verizon spokesman last week said the company plans to hook up all the connections needed to improve its service by the end of the year.

Meantime, Verizon points out that Netflix could redirect some of its traffic to less congested routes. But that could increase data-transit costs for the streaming-video company.

“What we’re saying is that the company needs to use a little more discretion in the middleman they choose,” Bob Elek, the Verizon spokesman, said Monday. “It’s really up to them to make sure that the content that they’re sending out is delivered in the most efficient manner possible. That doesn’t just go for Netflix. That goes for everyone.”

In a blog post Monday, Netflix said it doesn’t “purposely select congested routes” to send its traffic. “We pay some of the world’s largest transit networks to deliver Netflix video right to the front door of an ISP. Where the problem occurs is at that door — the interconnection point — when the broadband provider hasn’t provided enough capacity to accommodate the traffic their customer requested.”

Last week, Netflix and Verizon tussled over a message Netflix sent to consumers about degraded speeds. Verizon customers saw a message that said: “The Verizon network is crowded right now.” Verizon sent a cease-and-desist letter to Netflix dated Thursday, threatening the streaming video company with legal action over the claims.

In its blog post, Netflix said the test that spawned the message will end June 16, after which the company “will evaluate rolling it out more broadly.”

Netflix has been outspoken against the practice of broadband providers seeking money from Netflix and other Internet companies that want direct hookups to their networks for faster and smoother traffic streams to consumers. Netflix earlier this year agreed to pay Comcast, the largest broadband provider, for such a connection and has since complained that it was compelled to come to such terms due to degrading service quality for their shared customers.

In the latest set of rankings, Comcast also tumbled two spots. A person familiar with Netflix’s thinking said Comcast’s drop is related to “ongoing implementation of full interconnectivity between our networks.”

Comcast said that over the past couple of months, it has installed “multiple terabits per second of capacity” to support Netflix traffic. “We have monthly discussions with Netflix about capacity and performance and are constantly working to upgrade interconnections to support additional traffic based on forecasts,” a Comcast spokesman said in an emailed statement.

The biggest gainer was Charter Communications. Even though Charter doesn’t have a deal that allows Netflix direct access to its network, the cable company climbed two spots, entering the top three of major U.S. Internet providers.